Question

Sarah has a brother who is 5 years younger than herself and another brother who is 8 years younger than herself. She observes that the product of her brothers ages is equal to the age of her 40 year old father. How old is Sarah? How do we setup an equation for this using null factor law presumably.

Answer 1

Sarah is 13 years old

Explanation:

Represent Sarah's age with S

Her first brother's age with F

Her second brother's age with B

So, we have:

From the first statement, we have:

`S - F = 5` ---- (1)

From the second, we have:

`S - B = 8` ---- (2)

The product of their ages is 40.

First, we make F the subject in (1) and B the subject in (2)

`F = S - 5`

`B = S - 8`

Their product is represented as follows:

`F * B = 40`

Substitute values for F and B

`(S - 5) * (S - 8)=40`

Open bracket

`S^2 - 5S -8S + 40 = 40`

`S^2 - 13S + 40 = 40`

Subtract 40 from both sides

`S^2 - 13S = 0`

Factorize:

`S(S - 13) = 0`

Split:

`S = 0` or
`S - 13 = 0`

But Sarah's age can't be 0 because she has two younger brothers.

So, we stick to

`S - 13 = 0`

Make S the subject

`S = 13`

Hence, Sarah is 13 years old